Control method for single-phase grid-connected lcl inverter

ABSTRACT

A method of controlling the grid-side current of a single-phase grid-connected converter having an LCL filter connected between the output of the converter and the grid. The method includes measuring a grid voltage (v S ) and at least one signal in a group of signals consisting of a grid-side current (i 0 ), a converter-side current (i 1 ) and a capacitor voltage (v C0 ). The method includes estimating the fundamental component (v S,1 ) of the grid voltage (v S ), forming a grid-side current reference (i 0 *), a converter-side current reference (i 1 *) and a capacitor voltage reference (v C0 *) for the grid-side current of the LCL filter using the fundamental component of the grid voltage (v S,1 ), forming estimates for the non-measured signals in said group of signals, forming a grid-side current difference term (ĩ 0 ), a converter-side current difference term (ĩ 1 ) and a capacitor voltage difference term ({tilde over (v)} C0 ) from the differences between the references and measured/estimated values of said signals, forming an injection term for damping the resonance of the LCL filter by using an active damping injection mechanism (ADI), in which the grid-side current difference term (ĩ 0 ), the converter-side current difference term (ĩ 1 ) and the capacitor voltage difference term ({tilde over (v)} C0 ) are used, forming an estimate of harmonic distortion term ({circumflex over (φ)}) using the grid-side current difference term (ĩ 0 ), and controlling the output voltage (e) of the converter on the basis of the grid voltage, formed injection term and formed estimate of the harmonic distortion term ({circumflex over (φ)}) to produce a grid side (i 0 ) current corresponding to the current reference.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119 to European PatentApplication No. 10154113.4 filed in Europe on Feb. 19, 2010, the entirecontent of which is hereby incorporated by reference in its entirety.

FIELD

The present disclosure relates to controlling grid-connected converters.More particularly, the present disclosure relates to an arrangement inwhich an LCL filter is used as the interface between a voltage sourceinverter (VSI) and the grid.

BACKGROUND INFORMATION

The use of power converters in grid-connected applications has become apopular subject in the last few years. In distributed generationsystems, these power converters act as active interfaces, and can becomposed of a VSI connected to the grid by means of a simple series Lfilter. However, to avoid injection of switching harmonics, thissolution is limited to high switching frequencies. In contrast, it hasbeen observed that the use of inverters with LCL filters can achievereduced levels of harmonic distortion, even at low switching frequenciesand with a smaller inductance. Therefore, they have become a morecompact and economically more convenient solution. This makes theinverters with LCL filters good candidates for higher power applicationswhere the switching frequency is limited. The applicability of thesesystems includes static VAR compensators, uninterruptible power systems,power flow compensators, and distributed generation system interfaces(photovoltaic, wind power, micro turbine, fuel cell, etc.), amongothers. In distributed generation applications, the primary energysource is connected to the grid by means of a power converter, such as avoltage source inverter (VSI), and a filter. Originally, an L filter wasused, but recently LCL filter-based converters are becoming more populardue to their improved characteristics that allow them to comply with theincreasingly more restrictive standards. These systems, however, presentmore complex dynamics than L filter-based converters. Besides theincreased complexity of the LCL filter, a resonance arises, whichcompromises the stability of the system and makes the system moresusceptible to grid disturbances. Therefore, more sophisticatedcontroller methods are desired to guarantee stability with enhanceddisturbance rejection capability. In particular, the control schemesshould be able to alleviate the harmonics distortion which has become analmost mandatory feature for the controller design. Simultaneously, theimplementation of such controllers should be kept as simple as possibleand minimize or dispense with the requirement of additional sensors tokeep the implementation cost comparable to known L filter-basedconverters.

The present disclosure makes reference to thirteen (13) documentsidentified in the References section below. Each of these documents isincorporated by reference in their entireties. For conciseness, thedocuments are identified herein with respect to the numeral assignedthereto in the References section below. In document [1], the authorspresent a comparison between PV inverters with an L filter and with anLCL filter. They show that with both schemes the low frequency harmonicsattenuation is more and less the same. However, in the LCL filter, theswitching harmonics are better attenuated. For instance, the LCL filtermakes it possible to comply with EMC standards with relatively lowswitching frequencies. The authors observe that in LCL filters controlbecomes more expensive and complex. The proposed controller requiresmeasurement of all variables.

In document [2], the authors propose to use similar controllers for theLCL filter as in the L filter inverter. They consider that at lowfrequencies the response between a single L filter and an LCL filter issimilar. The authors use PI controllers for both the current and the DClink voltage controllers. Moreover, they propose to add a passiveresistor in parallel with the outer inductor to somehow improvestability at the cost of dissipation losses. The inverter is controlledto emulate a resistor so that the current will be a scaled version ofthe grid voltage. However, if the grid voltage is distorted, then thecurrent will also be distorted. The voltage outer loop is used toproduce the current reference, and thus its bandwidth is made very smallto avoid further distortion reinjection.

In document [3], the authors present a proportional-plus-resonant (P+R)controller. They measure the grid-side current and the capacitorcurrent. This is for a three-phase system. They study the effect of theharmonic distortion in the grid voltage, however, only to propose totune the controller to somehow alleviate this issue.

In document [4], the authors propose a controller which requires thatonly the current on the inverter side and the grid voltage are measured.The scheme is based on a P+R controller for the stability and trackingof the fundamental, and includes a bank of harmonic oscillators for thecompensation of harmonic distortion (HC). However, the proposed schemecontrols the inverter-side current rather than the grid current, andthus it may experience some inaccuracies on the delivered outputcurrent. The authors also propose to include the delay due to sampling,which apparently improves stability. Then, in documents [5] to [6], theyuse basically the same controller, except that this time they measurethe current on the grid side. However, direct application of thiscontroller to the grid current may entail stability issues as there ismissing damping that cannot be injected with a simple P+R controller.

It is clear that with the LCL filter, a resonance is introduced, andthus efforts should be made to somehow damp this resonance and preservestability. This process of damping the resonance is referred to asactive damping injection. Different approaches for active dampinginjection in LCL filters have been proposed so far in documents [7] to[10].

In document [7], the authors propose the use of a lead-lag compensatorloop on the capacitor voltage to actively damp the resonance of the LCLfilter. Other works use the feedback of the capacitor current (document[10]), and some others require the feedback of all state variables ofthe LCL filter (document [9]). However, the use of additionalmeasurements increases the cost as more sensors are required. Theintroduction of complex poles and complex zeros, as well as theintroduction of a notch filter around the resonance, are also othertechniques reported in document [8]. However, as noticed by the authors,the tuning of such schemes is sensitive to system parameters, and theactive damping injection could become ineffective in case of a weakgrid.

In document [8], the authors propose the use of a P+R as the currentcontroller. They realize that in the low frequencies range, thestability conditions are imposed mainly by the P+R controller. However,at high frequencies, stability is more related to the damping of the LCLfilter itself, with very small influence from the P+R controller. Thismotivates the use of mechanisms to insert extra damping so stability canbe guaranteed. The authors propose to inject active damping by insertingtwo zeros around the resonance frequency. Moreover, in the case that theconverter current is the measured variable, they propose to include twoactive damping poles to somehow compensate the resonant zeros of thesystem. They also study another method that consists of inserting anotch filter around the system resonance. The authors show that in caseof a weak grid, the active damping injection could be ineffective, andthus provisions must be taken to properly tune the controller.

In document [9], the authors propose a controller which is a cascadeinterconnection of PI and deadbeat controllers. The PI is used as anouter loop to control the grid current, delivering the reference for theinverter-side current, which is then stabilized by the deadbeatcontroller. The controller requires the measurements of all variables inthe LCL filter, and thus their feedback on the controller represents thestabilization mechanism. The effect of the harmonic distortion in thegrid voltage is studied, but no harmonic mechanism is included toovercome this issue. Rather, this compensation is left to the frequencycharacteristics of the cascade controller.

In document [10], the authors propose modifications to the conventionalDPC control to consider the LCL filter. They propose to alleviate theresonance issue by injecting active damping. For this purpose, thecapacitor current is measured in addition to the converter-side current.A harmonic compensation scheme is also presented, which is based on thesynchronous reference frame representations of signals.

SUMMARY

An exemplary embodiment of the present disclosure provides a method ofcontrolling the grid-side current of a single-phase grid-connectedconverter having an LCL filter connected between an output of theconverter and the grid. The method includes the steps of: measuring agrid voltage (v_(S)) and at least one signal in a group of signalsconsisting of a grid-side current (i₀), a converter-side current (i₁)and a capacitor voltage (v_(C0)); estimating a fundamental component(v_(S,1)) of the grid voltage (v_(S)); forming a grid-side currentreference (i₀*), a converter-side current reference (i₁*) and acapacitor voltage reference (v_(C0)*) for the grid-side current of theLCL filter using the estimated fundamental component of the grid voltage(v_(S,1)); forming estimates for any of the non-measured signals in saidgroup of signals; forming a grid-side current difference term (ĩ₀), aconverter-side current difference term (ĩ₁) and a capacitor voltagedifference term ({tilde over (v)}_(C0)) from the differences betweenreferences and the measured and/or estimated values of said signals;forming an injection term for damping the resonance of the LCL filter byusing an active damping injection mechanism (ADI), in which thegrid-side current difference term (ĩ₀), the converter-side currentdifference term (ĩ₁) and the capacitor voltage difference term ({tildeover (v)}_(C0)) are used; forming an estimate of a harmonic distortionterm ({circumflex over (φ)}) using the grid-side current difference term(ĩ₀); and controlling the output voltage (e) of the converter on thebasis of the grid voltage, formed injection term and formed estimate ofthe harmonic distortion term ({circumflex over (φ)}) to produce a gridside (i₀) current corresponding to the current reference.

An exemplary embodiment provides a converter in association with a LCLfilter. The exemplary converter includes: means for measuring a gridvoltage (v_(S)) and at least one signal in a group of signals consistingof a grid-side current (i₀), a converter-side current (i₁) and acapacitor voltage (v_(C0)); means for estimating a fundamental component(v_(S,1)) of the grid voltage (v_(S)); means for forming a grid-sidecurrent reference (i₀*), a converter-side current reference (i₁*) and acapacitor voltage reference (v_(C0)) for the grid-side current of theLCL filter using the estimated fundamental component of the grid voltage(v_(S,1)); means for forming estimates for any of the non-measuredsignals in said group of signals; means for forming a grid-side currentdifference term (ĩ₀), a converter-side current difference term (ĩ₁) anda capacitor voltage difference term ({tilde over (v)}_(C0)) from thedifferences between the references and measured/estimated values of saidsignals; means for forming an injection term for damping the resonanceof the LCL filter by using an active damping injection mechanism (ADI),in which the grid-side current difference term (ĩ₀), the converter-sidecurrent difference term (ĩ₁) and the capacitor voltage difference term({tilde over (v)}_(C0)) are used; means for forming an estimate of aharmonic distortion term ({circumflex over (φ)}) using the grid-sidecurrent difference term (ĩ₀); and means for controlling the outputvoltage (e) of the converter on the basis of the grid voltage, formedinjection term and formed estimate of the harmonic distortion term({circumflex over (φ)}) for producing a grid side (i₀) currentcorresponding to the current reference.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional refinements, advantages and features of the presentdisclosure are described in more detail below with reference toexemplary embodiments illustrated in the drawings, in which:

FIG. 1 illustrates a single-phase inverter grid-connected through an LCLfilter, according to an exemplary embodiment of the present disclosure;

FIG. 2 illustrates a block diagram representation of the LCL filterwhere the inverter-side current is considered as output, according to anexemplary embodiment of the present disclosure;

FIG. 3 illustrates a block diagram of an exemplary control methodaccording to the present disclosure;

FIG. 4 illustrates an exemplary embodiment of the fundamental quadraturesignals generator (F-QSG) which is used to reconstruct the fundamentalharmonic component of the grid voltage {circumflex over (v)}_(S,1);

FIG. 5 illustrates a block diagram representation of the LCL filter thegrid-side current is considered as output, according to an exemplaryembodiment of the present disclosure;

FIG. 6 illustrates the frequency responses of an ADI scheme for the LCLgrid-connected inverter, according to an exemplary embodiment of thepresent disclosure;

FIG. 7 illustrates the location of the poles before and after the ADIscheme is included in the LCL grid-connected inverter, according to anexemplary embodiment of the present disclosure;

FIG. 8 illustrates a feedback loop of an HCM based on a bank of QSGs,whose design follows the internal model principle, according to anexemplary embodiment of the present disclosure;

FIG. 9 illustrates the frequency responses of an ADI+HC scheme for theLCL grid-connected inverter, according to an exemplary embodiment of thepresent disclosure;

FIG. 10 illustrates an exemplary embodiment of the harmonic compensatormechanism HCM based on the concept of the k-th harmonic quadraticsignals generator kth-QSG reconstructing the disturbance {circumflexover (φ)};

FIG. 11 illustrates the interconnection of the reduced order observer(R-OBS) and the plant, according to an exemplary embodiment of thepresent disclosure;

FIG. 12 illustrates an exemplary embodiment of the ADI+HC scheme and theplant;

FIG. 13 illustrates the grid-side current i₀ tracking pure sinusoidalsignal in phase with the grid voltage v_(S) in the steady state,according to an exemplary embodiment of the present disclosure;

FIG. 14 illustrates that the shape of the grid-side current i₀ duringstep changes in the grid irradiation, according to an exemplaryembodiment of the present disclosure;

FIG. 15 illustrates the estimate of the fundamental component{circumflex over (v)}_(S,1) of the grid voltage, according to anexemplary embodiment of the present disclosure;

FIG. 16 illustrates the transient of the grid-side current i₀, grid-sidecurrent estimate î₀, capacitor voltage v_(C0) and capacitor voltageestimate {circumflex over (v)}_(C0) at the start up, according to anexemplary embodiment of the present disclosure;

FIG. 17 illustrates the error between the real grid current i₀ and itsreference i₀* after a relatively short transient, according to anexemplary embodiment of the present disclosure;

FIG. 18 illustrates transients due to the irradiation changes, accordingto an exemplary embodiment of the present disclosure;

FIG. 19 illustrates transients of the grid-side current observationerror (i₀−î₀) during step changes in irradiation, according to anexemplary embodiment of the present disclosure;

FIG. 20 which illustrates transients during step changes in irradiation,according to an exemplary embodiment of the present disclosure.

DETAILED DESCRIPTION

Exemplary embodiments of the present disclosure provide a method ofcontrolling the grid-side current of a single-phase-grid-connectedconverter having an LCL filter connected between the output of theconverter and the grid. Exemplary embodiments of the present disclosurealso provide such a converter in association with a LCL filter.

Exemplary embodiments of the present disclosure are based on the idea ofintroducing an active damping injection (ADI) and a harmonicscompensation mechanism (HCM) to a control method for controlling thecurrent of a single-phase inverter connected to the grid through an LCLfilter. The active damping injection (ADI) damps the resonance of theLCL filter, and the harmonic compensation mechanism (HCM) copes withharmonic distortion present in the grid voltage. The control methoddesign is based on the model structure, and thus the information of thedynamical structure is incorporated in the method to allow betterdynamical performances. The exemplary method also includes a feedbackcontrol loop to inject the required active damping (ADI). According toan exemplary embodiment, not all required quantities are measured.Accordingly, an observer can be used to form estimates of thenon-measured signals. For instance, if only the inverter-side current ismeasured, a reducer order observer (R-OBS) may also be included toreconstruct the non-available states. The R-OBS uses information on themeasured inverter-side current, grid voltage, and injected voltagesignal produced by the inverter. The use of observed variables in theplace of non-available states for control implementation is wellsupported by the separation principle. The harmonic compensationmechanism (HCM) is formed by a set of quadratic signals generators(QSGs) where the fundamental frequency enters as an input variable.

In accordance with exemplary embodiments of the present disclosure, thegrid-side current is controlled directly, which makes the systemresponse less sensitive to disturbances on the grid side, and guaranteesa cleaner response of the grid-side current. Furthermore, in accordancewith exemplary embodiments of the present disclosure, no additionalsensors are required, thus maintaining an easy implementation withoutextra costs. Moreover, in accordance with exemplary embodiments of themethod and converter disclosed herein, the converter functions properlyin cases of variation of the fundamental frequency since the harmoniccompensation mechanism (HCM) uses the fundamental frequency as an inputvariable. The value of the fundamental frequency can be generated by anexternal scheme such as a PLL scheme.

The present disclosure concentrates on the current control of agrid-connected LCL inverter. That is, the control method according to anexemplary embodiment of the present disclosure generates an expressionfor the injected voltage e, which can then be reproduced by a suitablevoltage source inverter (VSI) connected to a DC voltage source and basedon an appropriate modulation algorithm. It is important to remark thatthe technique works for any topology of a voltage source inverter (VSI)able to reproduce signal e and any DC voltage source or primary energysource. The latter includes alternative energy sources with or withoutan additional converter or passive energy storage elements which areable to provide a constant DC voltage to the voltage source inverter(VSI). Therefore, signal e is considered thorough this document as thecontrol input signal.

FIG. 1 is illustrates an exemplary embodiment of a single-phase inverter1 connected to a grid 2 through an LCL filter 3. The inverter 1 has a DCvoltage source 4 as an energy source. The mathematical model of thegrid-connected LCL inverter 1+3 is

L ₁{circumflex over ({dot over (i)}₁ =−v _(C0) +e

C ₀ {dot over (v)} _(C0) =i ₁ −i ₀

L ₀{circumflex over ({dot over (i)}₀ =v _(C0) −v _(S)  (1)

where i₁ is the current of inductor L₁, also referred to as theinverter-side current or the converter-side current; i₀ is the currentof inductor L₀, also referred as the grid-side current; v_(C0) is thevoltage in the capacitor C₀; and v_(S) is the grid voltage.

For control design purposes, the following main assumptions are made:

The parameters L₁, L₀ and C₀ are known and

The grid voltage v_(S) is a distorted signal containing higher orderharmonics of the fundamental frequency ω₀.

A block diagram representation of this system is shown in FIG. 2. Itrepresents a linear time-invariant (LTI) third order system 10 having asa control input the signal e, and as output the signal i₁. The gridvoltage v_(S) acts as an external disturbance. The injected voltage eand the grid voltage v_(S) transfer functions are represented by terms10.1 and 10.2, respectively, in FIG. 2.

The control objective includes obtaining an expression for the controlinput e such that the current on the grid side i₀ follows a referencei₀* proportional to the fundamental component of the grid voltagev_(S,1), that is,

$\begin{matrix}{{i_{0}->i_{0}^{*}}{i_{0}^{*} = {\frac{P}{v_{S,{RMS}}^{2}}v_{S,1}}}} & (2)\end{matrix}$

where v_(S,RMS) is the root mean square (RMS) value of v_(S). Thescaling factor 1/v_(S,RMS) ² is included to avoid numerical errors onlyand thus an exact value is not required; scalar P represents themodulation amplitude of the current reference i₀*. In fact, P gives anapproximate of the delivered power, and is computed by a suitable outercontrol loop. In case of alternative energy sources, the outer loopgenerates P to guarantee operation on the maximum power point (MPP).However, the design of the outer loop is outside the scope of thepresent disclosure, and thus P is assumed available. It is also assumedthat the dynamics on this outer loop are considerably slower than thedynamics of the LCL filter and thus, on the basis of a scale separationprinciple, the scalar P can be viewed as a constant in the dynamics ofthe LCL filter.

The tracking objective described above becomes even more challenging, ifa grid voltage v_(S) perturbed with harmonic distortion is considered.This operation condition may cause two issues: first, the currentreference i₀* will be contaminated by harmonics; and second, thedistortion of the grid voltage v_(S) will be propagated to all signalson the LCL filter, for example to the grid-side current i₀. To overcomethese issues, first a scheme insensitive to harmonic distortion isrequired to extract only the fundamental component of the grid voltage.Once a clean current reference is guaranteed, a controller can bedesigned that incorporates a harmonic compensation mechanism to cancelthe effect of the harmonic distortion in the grid voltage. As a result,the system will be able to deliver a pure sinusoidal current signal tothe grid.

A block diagram of the control method according to an exemplaryembodiment of the present disclosure is shown in FIG. 3. The LCL filter20 is connected to a control system 21 for carrying out the controlmethod according to the present disclosure. The control method incontrol system 21 in FIG. 12 includes a reference generation phase 21.1.A grid-side current reference i₀*, a converter-side current referencei₁* and a capacitor voltage reference v_(C0)* are formed in thereference generation phase 21.1.

The grid-side current reference i₀* defined in (1) requires knowledge ofthe fundamental component v_(S,1), which is not available. Differentmethods can be used to extract or estimate the fundamental component ofthe grid voltage v_(S), and perhaps an estimate of the fundamentalfrequency. The last is especially useful in the case that thefundamental frequency is not known or varies slowly with time. These arethe functions of any phase-locked loop (PLL) scheme, and thus any PLLscheme can be used for this purpose.

In some embodiments a very basic PLL scheme for the estimation of thefundamental component of the grid voltage v_(S) can be used. It assumesthat the fundamental frequency ω₀ is available. The expressions of thisestimator are

{circumflex over ({dot over (v)} _(S,1)=ω₀{circumflex over(φ)}_(S,1)+λ₁(v _(S) −{circumflex over (v)} _(S,1))

{circumflex over ({dot over (φ)}_(S,1)=−ω₀ {circumflex over (v)}_(S,1)  (3)

where λ₁ is a positive design parameter referred to as the estimationgain. This estimator is referred to as the fundamental quadraturesignals generator (F-QSG), as it generates estimates for the fundamentalcomponent v_(S,1) of the grid voltage and its quadrature companionsignal φ_(S,1). FIG. 4 illustrates a block diagram embodying thefundamental quadrature signals generator (F-QSG), according to anexemplary embodiment of the present disclosure. The F-QSG 30 in FIG. 4includes two integrators 30.1 and 30.2. The first integrator 30.1produces the fundamental component v_(S,1) of the grid voltage, and thesecond integrator 30.2 produces the quadrature companion signal φ_(S,1).The opposite value of the first integrator 30.1 output multiplied by thefundamental frequency ω₀ is used as the input for the second integrator30.2. The input for the first integrator 30.1 is produced by determiningthe difference {tilde over (v)}_(S) between the grid voltage v_(S) andthe output of the first integrator 30.1, multiplying the difference{tilde over (v)}_(S) with the estimation gain λ₁, and adding the productof the output of the second integrator 30.2 and the fundamentalfrequency ω₀ to the product of the difference {tilde over (v)}_(S) withthe estimation gain λ₁.

Returning to FIG. 3, the grid-side current reference i₀* can thus becomputed as

$\begin{matrix}{i_{0}^{*} = {\frac{P}{v_{S,{RMS}}^{2}}{\hat{v}}_{S,1}}} & (4)\end{matrix}$

and in case of requiring reactive power injection, the followingreference can be used:

$\begin{matrix}{i_{0}^{*} = {{\frac{P}{v_{S,{RMS}}^{2}}{\hat{v}}_{S,1}} + {\frac{Q}{v_{S,{RMS}}^{2}}{\hat{\phi}}_{S,1}}}} & (5)\end{matrix}$

where Q represents the desired reactive power to be injected.

According to an exemplary embodiment, the main interest of thecontroller is to guarantee tracking of the grid-side current i₀ towardsits reference i₀* only. That is, the tracking of the other variablestowards their corresponding references is not crucial, as long as theyremain bounded, and thus the controller can be further simplified byapproximating the references for i₁* and v_(C0)* as follows

v_(C0)*≅{circumflex over (v)}_(S,1)

i₁*≅i₀*+ω₀C₀{circumflex over (φ)}_(S,1)  (6)

and by relaying in the harmonic compensation capability of a harmonicscompensation mechanism (HCM), which must be able to absorb the termsthat have been neglected from the references (6) above. The harmonicscompensation mechanism (HCM) is discussed in more detail later on inthis document. The term ω₀C₀{circumflex over (φ)}_(S,1) is preserved fori₁* as this term has a considerable value incorporating the necessaryphase shift to i₁, which may have a positive effect during transients.

The active damping injection part 21.2 in FIG. 3 includes means forforming an injection term for damping the resonance of the LCL filter byusing an active damping injection mechanism (ADI). In an exemplaryembodiment of the present disclosure, the separation principle [11] canbe used for this part of the controller design. It allows toindependently design the controller in two parts: a full state feedbackpart, which is based on the assumption that all the state variables areavailable; and an observer part, to estimate the non-available states.Then, in the controller implementation, the unavailable variables arereplaced by their estimates. The observer design is discussed later onthis document.

The control objective includes the design of e to guarantee perfecttracking of the grid-side current i₀ towards a pure sinusoidal referencei₀*=P{circumflex over (v)}_(S,1)/v_(S,RMS) ² despite of the existence ofharmonic distortion in the grid voltage v_(S), i.e., with harmonicrejection capability. Therefore, appealing to the separation principle[11], the grid-side current i₀ is considered to be available. Acontroller is designed to guarantee tracking on this variable.

FIG. 5 illustrates a block diagram of an exemplary embodiment of the LCLsystem 40 having as an output the grid-side current i₀ and the injectedvoltage e as a control input. The grid voltage v_(S) enters as anexternal disturbance. The injected voltage e and the grid voltage v_(S)transfer functions are represented by terms 40.1 and 40.2, respectively.This undamped system contains two poles on the imaginary axis located at±jω_(res), and a pole in the origin, with the natural resonancefrequency ω_(res) being given as

$\begin{matrix}{\omega_{res} = \sqrt{\frac{L_{0} + L_{1}}{L_{0}C_{0}L_{1}}}} & (7)\end{matrix}$

A controller that stabilizes the exemplary system in FIG. 5 is given as

e=v _(S) −φ−L ₀ C ₀ L ₁(a ₂ {tilde over (ï)} ₀ +a ₁ {tilde over ({dotover (i)} ₀ +a ₀ĩ₀)  (8)

where ĩ₀=i₀−i₀*, with i₀*=P{circumflex over (v)}_(S,1)/v_(S,RMS) ² asdefined before; a₀, a₁ and a₂ are positive design parameters used tointroduce the required damping to guarantee stability. This procedure isknown in the literature of power electronics as active dampinginjection, as the damping is injected without the need of passiveelements. It can be shown that this controller guarantees exponentialstability provided that

$\begin{matrix}{{{\frac{L_{1} + L_{0}}{L_{0}C_{0}L_{1}} + a_{1}} > \frac{\alpha_{0}}{a_{2}}};\mspace{14mu} {a_{2} > 0};\mspace{14mu} {a_{0} > 0.}} & (9)\end{matrix}$

The main drawback of this controller is that it requires the knowledgeof the harmonic distortion that has been concentrated in the single termφ, which is defined as

$\begin{matrix}{\varphi = {{{- \left( {L_{1} + L_{0}} \right)}\frac{P}{v_{S,{RMS}}^{2}}{\overset{.}{\hat{v}}}_{S,1}} - {C_{0}L_{1}{\overset{¨}{v}}_{S}} - {L_{0}C_{0}L_{1}\frac{P}{v_{S,{RMS}}^{2}}{\overset{\dddot{}}{\hat{v}}}_{S,1}}}} & (10)\end{matrix}$

FIG. 6 shows the frequency responses of the original undamped systemrepresented by curves 50.1 and 50.2 and of the closed loop systemrepresented by curves 51.1 and 51.2. After the introduction of themissing damping terms, the natural resonant peak of the LCL filter isconsiderably damped. As observed in the pole-zero map in FIG. 7, thepoles 60.1 and 60.2 in the imaginary axis, as well as the pole 60.3 inthe origin have all been shifted to the left to locations 61.1, 61.2 and61.3. For a first tuning approximation, the poles 61.1, 61.2 and 61.3 ofthe closed loop system are considered shifted to the left in such a waythat the poles 61.1 and 61.2, originally on the imaginary axis, are nowlocated at 0.1ω_(res)±j1.05ω_(res), and the pole 61.3, originally at theorigin, is now located at 0.4ω_(res), using the natural resonancefrequency ω_(res) of the original system. In other words, the real partsof the complex poles are placed at 1/10 of the resonance frequency, andthe real pole is moved four times farther than the real part of thecomplex poles. This allows the introduction of small damping whilepreserving stability even for considerable variations in the systemparameters. The control parameters can be tuned according to

a₀=0.25ω_(res) ³

a₁=0.05ω_(res) ²

a₂=0.45ω_(res)  (11)

The control method in the control system 21 in FIG. 3 also comprisesmeans 21.3 for compensating the harmonic distortion. In exemplaryembodiments where the harmonic distortion term φ is not known, thefollowing controller is used to replace harmonic distortion term φ byits estimate {circumflex over (φ)}

e=v _(S) −{circumflex over (φ)}−L ₀ C ₀ L ₁(a ₂ {tilde over (ï)} ₀ +a ₁{tilde over ({dot over (i)} ₀ +a ₀ ĩ ₀)  (12)

For the design of the variable {circumflex over (φ)}, the followingharmonic compensator mechanism (HCM) can be used:

$\begin{matrix}{\hat{\varphi} = {{\sum\limits_{k \in {\{{1,3,\; \ldots}\}}}{\hat{\varphi}}_{k}} = {\sum\limits_{k \in {\{{1,3,\; \ldots}\}}}{\frac{\gamma_{k}s}{s^{2} + {k^{2}\omega_{0}^{2}}}{\overset{\sim}{i}}_{0}}}}} & (13)\end{matrix}$

where γ_(k) is a positive design parameter representing the estimationgain for the kth harmonic component φ_(k), and kε{1, 3, 5, . . . }represents the indexes of the harmonics under concern. The set ofharmonic indexes usually includes the fundamental to guarantee trackingand the higher order harmonics of the grid voltage v_(S), for instancethe odd harmonics for harmonic cancellation. FIG. 8 illustrates a blockdiagram representation of the closed loop system 70 with the harmoniccompensator mechanism (HCM) 71, according to an exemplary embodiment ofthe present disclosure. The frequency response of the controlled systemis given in FIG. 9, where it can be observed that the effect of theharmonic compensator mechanism (HCM) is the introduction of notches atthe harmonics under concern. The solid curves 80.1 and 81.1 representthe closed loop system with the harmonic compensator mechanism (HCM),and the dashed curves 80.2 and 81.2 represent the original undampedsystem.

In exemplary embodiments where the fundamental frequency ω₀ is notknown, the implementation of the kth-QSG can be realized as follows

{circumflex over ({dot over (φ)}_(k) =kω ₀{circumflex over(ψ)}_(k)+γ_(k) ĩ ₀ , ∀kε{1,3,5, . . . }

{circumflex over ({dot over (ψ)}_(k) =−kω ₀φ_(k)  (14)

where ω₀ now represents an estimate of the fundamental frequency. Theestimation of ω₀ can be performed using a PLL scheme, for example. Anexemplary embodiment of the harmonic compensator mechanism (HCM) basedon this concept is shown in FIG. 10. The harmonic compensator mechanism(HCM) 90 in FIG. 10 is a bank of quadrature signals generators (QSG)90.1-90.k tuned at the harmonics under concern. Each QSG is referred toas the kth harmonic quadratic signals generator (kth-QSG). The QSG maybe implemented in a similar manner as the fundamental quadrature signalsgenerator (F-QSG). The fundamental frequency ω₀ is multiplied by the kvalue of the harmonic component under concern. The estimate of theharmonic disturbance {circumflex over (φ)} is composed by the sum ofharmonic components {circumflex over (φ)}_(k), kε{1, 3, 5, . . . }, eachgenerated with the corresponding kth-QSG, i.e.,

$\begin{matrix}{\hat{\varphi} = {\sum\limits_{k \in {\{{1,3,\; \ldots}\}}}{{\hat{\varphi}}_{k}.}}} & (15)\end{matrix}$

A first tuning rule for the estimation gains γ_(k) can be stated asfollows. At the low frequency range, the response of the remainingdynamics observed by the harmonic compensator mechanism (HCM) isbasically a first order system with a pole located at a higherfrequency. Disregarding, for simplicity, the influence of such afrequency response, the gain γ_(k) can be set as γ_(k)=2.2/T_(kr), whereT_(kr) is the desired response time for each harmonic component,evaluated between 10% and 90% of a step response of the amplitude of thecorresponding sinusoidal perturbation.

Returning to FIG. 3, the controller expression (12) can also be writtenin terms of more familiar variables rather than in terms of timederivatives of ĩ₀ as follows

e=v _(S) −{circumflex over (φ)}−a ₂ L ₁ ĩ ₁ −a ₁ L ₁ C ₀ {tilde over(v)} _(C0)−(a ₀ −a ₂ L ₁)ĩ ₀  (16)

where ĩ₁=i₁−i₁* and {tilde over (v)}_(C0)=v_(C0)−v_(C0)*. Thesedifference terms {tilde over (v)}_(C0) and ĩ₁ along with the differenceterm ĩ₀ can be produced from the references i₀*, i₁* and v_(C0)* andtheir counterpart measurements or estimates in the comparison phase 21.4of the control system 21 in FIG. 3.

As some signals used in the above controller are not available, it ispossible to reconstruct them by means of an observer, such as with theobserver 21.5 in FIG. 3. For instance, a reduced order observer (R-OBS)may be used. The conventional observer design method [11], or theImmersion and Invariance method (I&I) proposed in [12] can be used inthe observer design. Either method yields quite similar results.However, the Immersion and Invariance method (I&I) is regarded assimpler and in some cases yields simpler expressions.

In an embodiment including a reduced order observer (R-OBS) where thecapacitor voltage v_(C0) and the grid-side current i₀ used in the abovecontroller are not available, the observer dynamics can be given as

$\begin{matrix}{{{C_{0}{\overset{.}{\xi}}_{1}} = {{- {\alpha_{1}\left( {\xi_{1} - e} \right)}} - \xi_{2} + {\left( {{\frac{L_{1}}{C_{0}}\alpha_{1}^{2}} - {\frac{L_{1}}{L_{0}}\alpha_{2}} + 1} \right)i_{1}}}}{{L_{0}{\overset{.}{\xi}}_{2}} = {{\left( {1 + \alpha_{2}} \right)\left( {\xi_{1} - {\frac{L_{1}}{C_{0}}\alpha_{1}i_{1}}} \right)} - v_{S} - {\alpha_{2}e}}}} & (17)\end{matrix}$

where ξ₁ and ξ₂ are observer states and α₁ and α₂ are two designparameters. Then the signals can be reconstructed according to

$\begin{matrix}{{{\hat{v}}_{C\; 0} = {\xi_{1} - {\frac{L_{1}}{C_{0}}\alpha_{1}i_{1}}}}{{\hat{i}}_{0} = {\xi_{2} + {\frac{L_{1}}{L_{0}}\alpha_{2}i_{1}}}}} & (18)\end{matrix}$

where α₁ and α₂ should fulfill α₁>0 and 1+α₂>0 to guarantee that{circumflex over (v)}_(C0)→v_(C0), î₀→i₀ as t→∞ exponentially.

The ensemble of the observer dynamics (17) plus the expressions (18) toreconstruct the observed signals is referred to as the reduced orderobserver (R-OBS). FIG. 11 illustrates a block diagram of the connectionof the R-OBS 100 with the plant 10 which is the same as in FIG. 2. TheR-OBS 100 is divided into two parts: the observer dynamics 100.1 and thesignal reconstruction 100.2. In this exemplary embodiment, the observerimplementation requires the measured signals v_(S) and i₁, the controlsignal e, and the system parameters L₀, C₀ and L₁. The three parametersnow appear combined in the form of only two ratios L₁/L₀ and L₁/C₀. Thismay report some advantages regarding the robustness with respect toparameter uncertainties.

A first tuning rule based on the desired bandwidth ω_(BW) of theobserver can be used as follows

α₁=√{square root over (2)}ω_(BW)C₀

α₂=ω_(BW) ² L ₀ C ₀−1  (19)

In exemplary embodiments including a reduced order observer (R-OBS)where signals i₁ and v_(C0) are measured, the following simpler observerfor i₀ based on the Immersion and Invariance method (I&I) can be used

$\begin{matrix}{{{L_{0}{\overset{.}{\xi}}_{1}} = {{{- \alpha_{1}}\xi_{1}} + {\left( {1 + {\frac{C_{0}}{L_{0}}\alpha_{1}^{2}}} \right)v_{C\; 0}} + {\alpha_{1}i_{1}} - v_{S}}}{{\hat{i}}_{0} = {\xi_{1} - {\frac{C_{0}}{L_{0}}\alpha_{1}v_{C\; 0}}}}} & (20)\end{matrix}$

This observer does not require the knowledge of L₁. Moreover, the otherparameters appear as a single quotient C₀/L₀ which may represent anadvantage regarding the robustness against parameter uncertainties. Thepole of the observer dynamics is located at

$\begin{matrix}{\lambda_{1} = {- \frac{\alpha_{1}}{L_{0}}}} & (21)\end{matrix}$

which can be used for the tuning of parameter α₁.

In exemplary embodiments including a reduced order observer (R-OBS)where signals i₀ and v_(C0) are measured, based on the Immersion andInvariance method (I&I), the following simpler observer for i₁ can beused

$\begin{matrix}{{{L_{1}{\overset{.}{\xi}}_{1}} = {{{- \alpha_{1}}\xi_{1}} - {\left( {1 + {\frac{C_{0}}{L_{1}}\alpha_{1}^{2}}} \right)i_{1}} + {\alpha_{1}v_{C\; 0}} + e}}{{\hat{i}}_{1} = {\xi_{1} + {\frac{C_{0}}{L_{1}}\alpha_{i}i_{1}}}}} & (22)\end{matrix}$

In this case the pole of the observer dynamics is located at

$\begin{matrix}{\lambda_{1} = {- \frac{\alpha_{1}}{L_{1}}}} & (23)\end{matrix}$

which can be used for the tuning of parameter α₁. This observer does notdepend at all on the value of the grid-side inductance L₀. Other typesof observers may also be used in the method according to exemplaryembodiments of the present disclosure.

FIG. 12 illustrates a block diagram of an exemplary embodiment of thecontrol method according to the present disclosure. As in FIG. 2, theLCL filter 10 is represented by a sum of transfer functions, where thefirst term 10.1 represents the transfer function for the grid voltagev_(S), and the second term 10.2 represents the transfer function for theconverter produced voltage e. The subtraction of the terms 10.1 and 10.2produces the converter-side current i₁, which is measured and used inthe control method.

The reference generation in the control method 110 is performed by usinga fundamental quadrature signals generator (F-QSG) 110.1 to produce thefundamental component v_(S,1) of the grid voltage and its quadraturecompanion signal φ_(S,1). The fundamental quadrature signals generator(F-QSG) 110.1 is realized using equations (3). The control methodcomprises means 110.2 to 110.5 to produce the references i₀*, i₁* andv_(C0)* from the fundamental component v_(S,1) of the grid voltage v_(S)and its quadrature companion signal φ_(S,1) according equations (4, 6).

The harmonic compensation 110.6 can be performed by using a harmonicscompensation mechanism (HCM) described in equation (13). The harmoniccompensation mechanism (HCM) realization can be performed by usingequations (14).

The non-available signals v_(C0) and i₀ are replaced by their estimates{circumflex over (v)}_(C0) and î₀, respectively, using a reduced orderobserver 110.7, which can be realized according to equations (17 to 18).The replacement of the signals with their estimates is well supported bythe separation principle stated above.

The active damping injection mechanism (ADI) described in equation (16)is used to implement the active damping. This yields the followingexpression for the controller

$\begin{matrix}{{e = {v_{S} - \hat{\varphi} - {R_{2}\left( {i_{1} - i_{0}^{*} - {\omega_{0}C_{0}{\hat{\phi}}_{S,1}}} \right)} - {R_{1}\left( {{\hat{v}}_{C\; 0} - {\hat{v}}_{S,1}} \right)} - {R_{0}\left( {{\hat{i}}_{0} - i_{0}^{*}} \right)}}}\mspace{20mu} {\hat{\varphi} = {\sum\limits_{k \in {\{{1,3,\; \ldots}\}}}{\frac{\gamma_{k}s}{s^{2} + {k^{2}\omega_{0}^{2}}}\left( {{\hat{i}}_{0} - i_{0}^{*}} \right)}}}} & (24)\end{matrix}$

where gains R₁=a₂L₁, R₂=a₁L₁C₀ and R₀=a₀L₀C₀L₁−a₂L₁, which according to(9) must now fulfill the conditions

$\begin{matrix}{{{\frac{L_{0}}{L_{1}}\left( {1 + R_{2}} \right)} > \frac{R_{0}}{R_{1}}},\mspace{14mu} {R_{2} > 0},\mspace{14mu} {R_{1} > 0},\mspace{14mu} {{R_{0} + R_{1}} > 0}} & (25)\end{matrix}$

The new parameters are tuned according to (11) as follows

R₁=0.45ω_(res)L₁

R₂=0.05ω_(res) ²L₁C₀

R ₀=0.25ω_(res) ³ L ₀ C ₀ L ₁ −R ₁  (26)

According to (25), negative values for R₀ are allowed. In FIG. 12, theactive damping injection is realized using means 110.8 to 110.13.

According to an exemplary embodiment, any of the means describedhereinabove for implementing the described aspects of the method may,for example, be a processor, a DSP, or a programmable logic device(PLD), e.g., an FPGA. The processor and/or programmable logic device canexecute computer-readable instructions (e.g., a program) tangiblyrecorded on a non-transitory computer-readable recording medium, e.g., aROM, hard disk drive, optical memory, flash memory, etc.

For a simulation test, the single-phase photo-voltaic (PV) invertergrid-connected through an LCL filter of FIG. 1 is considered. Thissystem has been designed using the following parameters: L₁=2 mH, L₀=833μH, C₀=10 μF, C=2200 μF. The grid voltage v_(S) is described accordingto Table 1.

TABLE 1 Description of the grid voltage harmonic components. HarmonicAmplitude Phase No. [V_(RMS)] [deg] 1 230 0.0 3 50 14.3 5 25 8.6 7 155.7

The following parameters have been selected for the active damping partof the current controller: R₁=15, R₂=1, R₀=1, which follow the tuningguide-lines proposed in (26). For the harmonic compensation part, aselection is been made: γ₁=300, γ₃=200, γ₅=2 00, γ₇=200, whichcorrespond to T_(1r)=7.3 ms, and T_(3r)=T_(5r)=T_(7r)=11 ms,respectively. An estimator F-QSG with known ω₀, illustrated in FIG. 4,has been used instead of an adaptive scheme or a PLL, where the onlyparameter is tuned to λ₁=100, which corresponds to a T_(fr)=45 ms. Thedesign parameters for the observer have values α₁=−0.5 and α₂=0.1, whichcorrespond to (ω_(BW)=7071 r/s (approx. 1.1 KHz).

FIG. 13 shows that, in the steady state, the grid-side current i₀ tracksa pure sinusoidal signal in phase with the grid voltage v_(S), despitethe high distortion on the grid voltage. Then, FIG. 14 shows that theshape of the grid-side current i₀ remains sinusoidal, after an almostnegligible transient, during step changes in the grid irradiation from1000 W/m² to 500 W/m² (top part of FIG. 14) and back (bottom part ofFIG. 14).

FIG. 15 shows the estimate of the fundamental component {circumflex over(v)}_(S,1) of the grid voltage, according to an exemplary embodiment ofthe present disclosure. The estimate is built in the F-QSG. It is shownthat, after a relatively short transient during start up (top part ofFIG. 15), the estimate {circumflex over (v)}_(S,1) reaches the shape ofa pure sinusoidal signal. It can be observed that this estimate equalsthe real fundamental component v_(S,1) after the transient (bottom partof FIG. 15). All these take place in spite of the highly distorted gridvoltage v_(S).

FIG. 16 shows the transient of (top part of FIG. 16) the grid-sidecurrent i₀ and grid-side current estimate î₀, and (bottom part of FIG.16) capacitor voltage v_(C0) and capacitor voltage estimate {circumflexover (v)}_(C0) at the start up, according to an exemplary embodiment ofthe present disclosure. An initial condition different to zero wasintroduced intentionally in the observed states to see this transient.It is shown that the states are perfectly reconstructed after an almostimperceptible transient.

FIG. 17 shows that the error between the real grid current i₀ and itsreference i₀* reaches zero after a relatively short transient, accordingto an exemplary embodiment of the present disclosure. In this case, astep change is introduced in the irradiation going from 1000 W/m² to 500W/m² (top part of FIG. 17 at t=3 s) and back (bottom part of FIG. 17 att=4 s).

The corresponding power delivered by the PV is plotted in FIG. 18, wherethe transients due to the irradiation changes can be observed.

A 25% variation on the real grid-side inductance L₀ of the LCL filterhas been introduced intentionally to test the robustness of the proposedscheme to variations on this system parameter. In the controller thenominal value of this parameter is used. FIG. 19 illustrates transientsof the grid-side current observation error (i₀−î₀) during step changesin irradiation from 1000 W/m² to 500 W/m² (top part of FIG. 19) and back(bottom part of FIG. 19), according to an exemplary embodiment of thepresent disclosure. The difference between the real and the estimatedgrid-side currents, i.e., i₀−î₀ is no longer zero, but there is a rippleat the fundamental frequency. This means that the parameter mismatchcauses a slight phase shift with respect to the real value.

As a result, there is a slight phase shift between the real grid-sidecurrent i₀ and the grid voltage v_(S) as shown in FIG. 20 whichillustrates transients during a step change in irradiation (top part ofFIG. 20) from 1000 W/m² to 500 W/m² and back (bottom part of FIG. 20).

It will be obvious to a person skilled in the art that, as thetechnology advances, the inventive concept can be implemented in variousways. The disclosure and its embodiments are not limited to the examplesdescribed above but may vary within the scope of the claims.

It will be appreciated by those skilled in the art that the presentinvention can be embodied in other specific forms without departing fromthe spirit or essential characteristics thereof. The presently disclosedembodiments are therefore considered in all respects to be illustrativeand not restricted. The scope of the invention is indicated by theappended claims rather than the foregoing description and all changesthat come within the meaning and range and equivalence thereof areintended to be embraced therein.

REFERENCES

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1. A method of controlling the grid-side current of a single-phasegrid-connected converter having an LCL filter connected between anoutput of the converter and the grid, the method comprising the stepsof: measuring a grid voltage (v_(S)) and at least one signal in a groupof signals consisting of a grid-side current (i₀), a converter-sidecurrent (i₁) and a capacitor voltage (v_(C0)); estimating a fundamentalcomponent (v_(S,1)) of the grid voltage (v_(S)); forming a grid-sidecurrent reference (i₀*), a converter-side current reference (i₁*) and acapacitor voltage reference (v_(C0)*) for the grid-side current of theLCL filter using the estimated fundamental component of the grid voltage(v_(S,1)); forming estimates for any of the non-measured signals in saidgroup of signals; forming a grid-side current difference term (ĩ₀), aconverter-side current difference term (ĩ₁) and a capacitor voltagedifference term ({tilde over (v)}_(C0)) from the differences betweenreferences and the measured and/or estimated values of said signals;forming an injection term for damping the resonance of the LCL filter byusing an active damping injection mechanism (ADI), in which thegrid-side current difference term (ĩ₀), the converter-side currentdifference term (ĩ₁) and the capacitor voltage difference term ({tildeover (v)}_(C0)) are used; forming an estimate of a harmonic distortionterm ({circumflex over (φ)}) using the grid-side current difference term(ĩ₀); and controlling the output voltage (e) of the converter on thebasis of the grid voltage, formed injection term and formed estimate ofthe harmonic distortion term ({circumflex over (φ)}) to produce a gridside (i₀) current corresponding to the current reference.
 2. A method asclaimed in claim 1, wherein the fundamental frequency (ω₀) of the gridvoltage is known, and the estimating of the fundamental component(v_(S,1)) of the grid voltage comprises: determining a value for aquadrature companion signal (φ_(S,1)) by integrating the product of theopposite value of fundamental component of the grid voltage (v_(S,1))and the fundamental frequency of the grid voltage (ω₀); determining thedifference ({tilde over (v)}_(S)) between the grid voltage and thefundamental component of the grid voltage (v_(S,1)); adding the productof the quadrature companion signal (φ_(S,1)) and the fundamentalfrequency of the grid voltage (ω₀) to the product of the difference({tilde over (v)}_(S)) and the estimation gain (λ₁); and determining thevalue of the fundamental component of the grid voltage (v_(S,1)) byintegrating the sum of the addition.
 3. A method as claimed in claim 1,wherein the magnitude of the current reference (i₀*) for the grid-sidecurrent is proportional to an approximate of the delivered power (P). 4.A method as claimed in claim 1, wherein: the fundamental frequency (ω₀)of the grid voltage and the quadrature companion signal (φ_(S,1)) areknown; the capacitor voltage reference (v_(C0)*) is approximated by thefundamental component of the grid voltage (v_(S,1)); and theconverter-side current reference (i₁*) is approximated by the product ofthe capacitor capacitance (C₀), fundamental frequency (ω₀) and thequadrature companion signal (φ_(S,1)) added to the grid-side currentreference (i₀*).
 5. A method as claimed in claim 1, wherein theconverter-side current (i₁) is measured and the grid-side current (i₀)and the capacitor voltage (v_(C0)) are estimated using an observer,where the observer dynamics are given as:${C_{0}{\overset{.}{\xi}}_{1}} = {{- {\alpha_{1}\left( {\xi_{1} - e} \right)}} - \xi_{2} + {\left( {{\frac{L_{1}}{C_{0}}\alpha_{1}^{2}} - {\frac{L_{1}}{L_{0}}\alpha_{2}} + 1} \right)i_{1}}}$${{L_{0}{\overset{.}{\xi}}_{2}} = {{\left( {1 + \alpha_{2}} \right)\left( {\xi_{1} - {\frac{L_{1}}{C_{0}}\alpha_{1}i_{1}}} \right)} - v_{S} - {\alpha_{2}e}}},$where ξ₁ and ξ₂ are observer states, L₁ is the converter-side inductorinductance, C₀ is the capacitor capacitance and L₀ is the grid-sideinductor inductance of the LCL filter and ω_(res) is the naturalresonance frequency and a grid-side current estimate (î₀) and acapacitor voltage estimate ({circumflex over (v)}_(C0)) arereconstructed according to:${\hat{v}}_{C\; 0} = {\xi_{1} - {\frac{L_{1}}{C_{0}}\alpha_{1}i_{1}}}$${\hat{i}}_{0} = {\xi_{2} + {\frac{L_{1}}{L_{0}}\alpha_{2}i_{1}}}$where α₁ and α₂ are two design parameters which fulfill α₁>0 and 1+α₂>0.6. A method as claimed in claim 5, wherein the tuning of two designparameters α₁ and α₂ is based on a desired bandwidth (ω_(BW)) and saidparameters are tuned according to:α₁=√{square root over (2)}ω_(BW)C₀α₂=ω_(BW) ² L ₀ C ₀−1
 7. A method as claimed in claim 1, wherein theconverter-side current (i₁) and the capacitor voltage (v_(C0)) aremeasured and the grid-side current (i₀) is estimated using an observer,where the observer dynamics are given as:${L_{0}{\overset{.}{\xi}}_{1}} = {{{- \alpha_{1}}\xi_{1}} + {\left( {1 + {\frac{C_{0}}{L_{0}}\alpha_{1}^{2}}} \right)v_{C\; 0}} + {\alpha_{1}i_{1}} - {v_{S}.}}$where ξ₁ is an observer coefficient, C₀ is the capacitor capacitance andL₀ is the grid-side inductor inductance of the LCL filter and ω_(res) isthe natural resonance frequency, and a grid-side current estimate (î₀)is reconstructed according to:${\hat{i}}_{0} = {\xi_{1} - {\frac{C_{0}}{L_{0}}\alpha_{1}v_{C\; 0}}}$where α₁ is a design parameter.
 8. A method as claimed in claim 7,wherein the tuning of the design parameter α₁ is based on a desiredbandwidth (ω_(BW)), and said parameter is tuned according to:$\lambda_{1} = {- \frac{\alpha_{1}}{L_{0}}}$ where λ₁ is the pole of theobserver dynamics.
 9. A method as claimed in claim 1, wherein thegrid-side current (i₀) and the capacitor voltage (v_(C0)) are measuredand the converter-side current (i₁) is estimated using an observer,where the observer dynamics are given as:${{L_{1}{\overset{.}{\xi}}_{1}} = {{{- \alpha_{1}}\xi_{1}} - {\left( {1 + {\frac{C_{0}}{L_{1}}\alpha_{1}^{2}}} \right)i_{1}} + {\alpha_{1}v_{C\; 0}} + e}},$where ξ₁ is an observer coefficient, C₀ is the capacitor capacitance andL₁ is the converter-side inductor inductance of the LCL filter andω_(res) is the natural resonance frequency, and a grid-side currentestimate (î₀) is reconstructed according to:${\hat{i}}_{1} = {\xi_{1} + {\frac{C_{0}}{L_{1}}\alpha_{i}i_{1}}}$where α₁ is a design parameter.
 10. A method as claimed in claim 9,wherein the tuning of the design parameter α₁ is based on a desiredbandwidth (ω_(BW)), and said parameter is tuned according to:$\lambda_{1} = {- \frac{\alpha_{1}}{L_{1}}}$ where λ₁ is the pole of theobserver dynamics.
 11. A method as claimed in claim 1, wherein theforming of the injection term comprises: multiplying the grid-sidecurrent difference term (ĩ₀) by a constant R₀; multiplying theconverter-side current difference term (ĩ₁) by a constant R₁;multiplying the capacitor voltage difference term ({tilde over(v)}_(C0)) by a constant R₂; and forming the injection term by addingthe products together.
 12. A method as claimed in claim 11, wherein theconstants are defined asR₁=0.45ω_(res)L₁R₂=0.05ω_(res) ²L₁C₀R ₀=0.25ω_(res) ³ L ₀ C ₀ L ₁ −R ₁ where L₁ is the converter-sideinductor inductance, C₀ is the capacitor capacitance and L₀ is thegrid-side inductor inductance of the LCL filter and ω_(res) is thenatural resonance frequency.
 13. A method as claimed in claim 1, whereinthe forming of the estimate of the harmonic distortion term ({circumflexover (φ)}) comprises summation of k harmonic components ({circumflexover (φ)}₁−{circumflex over (φ)}_(k)).
 14. A method as claimed in claim1, wherein the fundamental frequency (ω₀) of the grid voltage is known,and forming of a harmonic component with an index number k ({circumflexover (φ)}_(k)) comprises: determining a value for a quadrature companionsignal ({circumflex over (ψ)}_(k)) by integrating the product of theopposite value of the harmonic component ({circumflex over (φ)}_(k)) andthe fundamental frequency (ω₀) of the grid voltage multiplied by thevalue of index number k; adding the product of quadrature companionsignal ({circumflex over (ψ)}_(k)) and the fundamental frequency of thegrid voltage (ω₀) multiplied by the fundamental frequency (ω₀) to theproduct of the grid-side current difference (ĩ₀) and the designparameter (γ_(k)); and determining the value of the harmonic component({circumflex over (φ)}) by integrating the sum of the addition.
 15. Amethod as claimed in claim 14, wherein the design parameter (γ_(k)) isset as γ_(k)=2.2/T_(kr), where T_(kr) is the desired response time foreach kth harmonic component, evaluated between 10% and 90% of a stepresponse of the amplitude of the corresponding sinusoidal perturbation.16. A method as claimed in claim 1, wherein the injection voltage (e) isformed by subtracting the estimate of harmonic distortion term({circumflex over (φ)}) and the injection term from the grid voltage(v_(S)).
 17. A converter in association with a LCL filter, the convertercomprising: means for measuring a grid voltage (v_(S)) and at least onesignal in a group of signals consisting of a grid-side current (i₀), aconverter-side current (i₁) and a capacitor voltage (v_(C0)); means forestimating a fundamental component (v_(S,1)) of the grid voltage(v_(S)); means for forming a grid-side current reference (i₀*), aconverter-side current reference (i₁*) and a capacitor voltage reference(v_(C0)*) for the grid-side current of the LCL filter using theestimated fundamental component of the grid voltage (v_(S,1)); means forforming estimates for any of the non-measured signals in said group ofsignals; means for forming a grid-side current difference term (ĩ₀) aconverter-side current difference term (ĩ₁) and a capacitor voltagedifference term ({tilde over (v)}_(C0)) from the differences between thereferences and measured/estimated values of said signals; means forforming an injection term for damping the resonance of the LCL filter byusing an active damping injection mechanism (ADI), in which thegrid-side current difference term (ĩ₀), the converter-side currentdifference term (ĩ₁) and the capacitor voltage difference term ({tildeover (v)}_(C0)) are used; means for forming an estimate of a harmonicdistortion term ({circumflex over (φ)}) using the grid-side currentdifference term (ĩ₀); and means for controlling the output voltage (e)of the converter on the basis of the grid voltage, formed injection termand formed estimate of the harmonic distortion term ({circumflex over(φ)}) for producing a grid side (i₀) current corresponding to thecurrent reference.
 18. A method as claimed in claim 2, wherein: thefundamental frequency (ω₀) of the grid voltage and the quadraturecompanion signal (φ_(S,1)) are known; the capacitor voltage reference(v_(C0)*) is approximated by the fundamental component of the gridvoltage (v_(S,1)); and the converter-side current reference (i₁*) isapproximated by the product of the capacitor capacitance (C₀),fundamental frequency (ω₀) and the quadrature companion signal (φ_(S,1))added to the grid-side current reference (i₀*).
 19. A method as claimedin claim 18, wherein the converter-side current (i₁) is measured and thegrid-side current (i₀) and the capacitor voltage (v_(C0)) are estimatedusing an observer, where the observer dynamics are given as:${C_{0}{\overset{.}{\xi}}_{1}} = {{- {\alpha_{1}\left( {\xi_{1} - e} \right)}} - \xi_{2} + {\left( {{\frac{L_{1}}{C_{0}}\alpha_{1}^{2}} - {\frac{L_{1}}{L_{0}}\alpha_{2}} + 1} \right)i_{1}}}$${{L_{0}{\overset{.}{\xi}}_{2}} = {{\left( {1 + \alpha_{2}} \right)\left( {\xi_{1} - {\frac{L_{1}}{C_{0}}\alpha_{1}i_{1}}} \right)} - v_{S} - {\alpha_{2}e}}},$where ξ₁ and ξ₂ are observer states, L₁ is the converter-side inductorinductance, C₀ is the capacitor capacitance and L₀ is the grid-sideinductor inductance of the LCL filter and ω_(res) is the naturalresonance frequency and a grid-side current estimate (î₀) and acapacitor voltage estimate ({circumflex over (v)}_(C0)) arereconstructed according to:${\hat{v}}_{C\; 0} = {\xi_{1} - {\frac{L_{1}}{C_{0}}\alpha_{1}i_{1}}}$${\hat{i}}_{0} = {\xi_{2} + {\frac{L_{1}}{L_{0}}\alpha_{2}i_{1}}}$where α₁ and α₂ are two design parameters which fulfill α₁>0 and 1+α₂>0.20. A method as claimed in claim 18, wherein the converter-side current)(i₁) and the capacitor voltage (v_(C0)) are measured and the grid-sidecurrent (i₀) is estimated using an observer, where the observer dynamicsare given as:${{L_{0}{\overset{.}{\xi}}_{1}} = {{{- \alpha_{1}}\xi_{1}} + {\left( {1 + {\frac{C_{0}}{L_{0}}\alpha_{1}^{2}}} \right)v_{C\; 0}} + {\alpha_{1}i_{1}} - v_{S}}},$where ξ₁ is an observer coefficient, C₀ is the capacitor capacitance andL₀ is the grid-side inductor inductance of the LCL filter and ω_(res) isthe natural resonance frequency and a grid-side current estimate (î₀) isreconstructed according to:${\hat{i}}_{0} = {\xi_{1} - {\frac{C_{0}}{L_{0}}\alpha_{1}v_{C\; 0}}}$where α₁ is a design parameter.
 21. A method as claimed in claim 18,wherein the grid-side current (i₀) and the capacitor voltage (v_(C0))are measured and the converter-side current (i₁) is estimated using anobserver, where the observer dynamics are given as:${{L_{1}{\overset{.}{\xi}}_{1}} = {{{- \alpha_{1}}\xi_{1}} - {\left( {1 + {\frac{C_{0}}{L_{1}}\alpha_{1}^{2}}} \right)i_{1}} + {\alpha_{1}v_{C\; 0}} + e}},$where ξ₁ is an observer coefficient, C₀ is the capacitor capacitance andL₁ is the converter-side inductor inductance of the LCL filter andω_(res) is the natural resonance frequency, and a grid-side currentestimate (î₀) is reconstructed according to:${\hat{i}}_{1} = {\xi_{1} + {\frac{C_{0}}{L_{1}}\alpha_{i}i_{1}}}$where α₁ is a design parameter.
 22. A method as claimed in claim 18,wherein the forming of the injection term comprises: multiplying thegrid-side current difference term (ĩ₀) by a constant R₀; multiplying theconverter-side current difference term (ĩ₁) by a constant R₁;multiplying the capacitor voltage difference term (v_(C0)) by a constantR₂; and forming the injection term by adding the products together, andwherein the constants are defined asR₁=0.45ω_(res)L₁R₂=0.05ω_(res) ²L₁C₀R ₀=0.25ω_(res) ³ L ₀ C ₀ L ₁ −R ₁ where L₁ is the converter-sideinductor inductance, C₀ is the capacitor capacitance and L₀ is thegrid-side inductor inductance of the LCL filter and ω_(res) is thenatural resonance frequency.
 23. A method as claimed in claim 18,wherein the forming of the estimate of the harmonic distortion term({circumflex over (φ)}) comprises summation of k harmonic components({circumflex over (φ)}₁−{circumflex over (φ)}_(k)).
 24. A method asclaimed in claim 15, wherein the injection voltage (e) is formed bysubtracting the estimate of harmonic distortion term ({circumflex over(φ)}) and the injection term from the grid voltage (v_(S)).